Division algebras with common subfields

Daniel Krashen; Eliyahu Matzri; Andrei Rapinchuk; Louis Rowen; David Saltman

doi:10.1007/s00229-021-01315-5

Division algebras with common subfields

Daniel Krashen
, Eliyahu Matzri
, Andrei Rapinchuk
, Louis Rowen
, David Saltman

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study the partial ordering on isomorphism classes of central simple algebras over a given field F, defined by setting A₁≤ A₂ if deg A₁= deg A₂ and every étale subalgebra of A₁ is isomorphic to a subalgebra of A₂, and generalizations of this notion to algebras with involution. In particular, we show that this partial ordering is invariant under passing to the completion of the base field with respect to a discrete valuation, and we explore how this partial ordering relates to the exponents of algebras.

Original language	English
Pages (from-to)	209-249
Number of pages	41
Journal	Manuscripta Mathematica
Volume	169
Issue number	1-2
DOIs	https://doi.org/10.1007/s00229-021-01315-5
State	Published - 1 Sep 2022
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/s00229-021-01315-5

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AU - Krashen, Daniel

AU - Matzri, Eliyahu

AU - Rapinchuk, Andrei

AU - Rowen, Louis

AU - Saltman, David

PY - 2022/9/1

Y1 - 2022/9/1

N2 - We study the partial ordering on isomorphism classes of central simple algebras over a given field F, defined by setting A1≤ A2 if deg A1= deg A2 and every étale subalgebra of A1 is isomorphic to a subalgebra of A2, and generalizations of this notion to algebras with involution. In particular, we show that this partial ordering is invariant under passing to the completion of the base field with respect to a discrete valuation, and we explore how this partial ordering relates to the exponents of algebras.

AB - We study the partial ordering on isomorphism classes of central simple algebras over a given field F, defined by setting A1≤ A2 if deg A1= deg A2 and every étale subalgebra of A1 is isomorphic to a subalgebra of A2, and generalizations of this notion to algebras with involution. In particular, we show that this partial ordering is invariant under passing to the completion of the base field with respect to a discrete valuation, and we explore how this partial ordering relates to the exponents of algebras.

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Division algebras with common subfields

Abstract

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